A scattering quantum circuit for measuring Bell's time inequality: a nuclear magnetic resonance demonstration using maximally mixed states

TL;DR

This paper demonstrates a quantum scattering circuit using nuclear magnetic resonance to measure time correlations in maximally mixed states, successfully violating Bell's time inequality and confirming quantum mechanical predictions.

Contribution

It introduces a novel quantum scattering circuit for noninvasive measurements on maximally mixed states, demonstrated via NMR, to test Bell's time inequality.

Findings

Observed violation of Bell's time inequality in NMR experiments.

Circuit accurately measures time correlations in maximally mixed states.

Results align with quantum mechanical predictions.

Abstract

In 1985, Leggett and Garg (1985 Phys. Rev. Lett. 54 857) proposed a Bell-like inequality to test (in)compatibility between two fundamental concepts of quantum mechanics. The first concept is 'macroscopic realism', which is the quality of a physical property of a quantum system being independent of observation at the macroscopic level. The second concept is 'noninvasive measurability', which is the possibility of performing a measurement without disturbing the subsequent evolution of a system. One of the key requirement for testing the violation of the Leggett-Garg inequality, or Bell's time inequality, is the ability to perform noninvasive measurements over a qubit state. In this paper, we present a quantum scattering circuit that implements such a measurement for maximally mixed states. The operation of the circuit is demonstrated using liquid-state nuclear magnetic resonance (NMR) in chloroform, in which the time correlations of a qubit are measured on a probe (ancillary) qubit state. The results clearly show a violation region and are in excellent agreement with the predictions of quantum mechanics.